If each of the observations x_1, x_2, ldots, | vedclass

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(B) Let the original observations be $x_1, x_2, \ldots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$. If e

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does not change

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(B) Let the original observations be $x_1, x_2, \ldots, x_n$. The variance is given by $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$. If each observation is increased or decreased by $k$,the new observations are $y_i = x_i \pm k$. The new mean becomes $\bar{y} = \frac{1}{n} \sum (x_i \pm k) = \bar{x} \pm k$. The new variance is $\sigma_y^2 = \frac{1}{n} \sum (y_i - \bar{y})^2 = \frac{1}{n} \sum ((x_i \pm k) - (\bar{x} \pm k))^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 = \sigma^2$. Thus,the variance remains unchanged.

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

If each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:

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